Find the measures of center—mean, median, and mode—for the given dataset.
10, 17, 11, 24, 12, 7, 15, 17, 20, 5, 11, 21, 16, 17
(2 points)
mean: ; median: ; mode:
To find the measures of center for the given dataset: 10, 17, 11, 24, 12, 7, 15, 17, 20, 5, 11, 21, 16, 17
1. Mean: The mean is the sum of all the numbers in the dataset divided by the total count of numbers.
- Sum of all the numbers = 10 + 17 + 11 + 24 + 12 + 7 + 15 + 17 + 20 + 5 + 11 + 21 + 16 + 17 = 198
- There are 14 numbers in the dataset.
- Mean = 198 / 14 = 14.14 (rounded to two decimal places)
2. Median: The median is the middle value of a dataset when the numbers are arranged in ascending or descending order.
- First, arrange the numbers in ascending order: 5, 7, 10, 11, 11, 12, 15, 16, 17, 17, 17, 20, 21, 24
- Since there are an even number of values, there are two middle values: 11 and 12.
- Median = (11 + 12) / 2 = 11.5
3. Mode: The mode is the number(s) that appear(s) most frequently in the dataset.
- In this case, the number 17 appears 3 times, which is more than any other number.
- Mode = 17
Therefore, the measures of center for the given dataset are:
Mean: 14.14
Median: 11.5
Mode: 17